INSTRUCTIONS Although system inputs are shown with different symbols for each projects, in instructions section, they are symbolized by u(t). Similarly, regardless of which letters are used on the project pages, system outputs are indicated by y (t), system states are specified by (t), where k = 1,2,...,n (n is the number of states). Furthermore, reference inputs to closed-loop control systems are denoted by r (t). PART #1: MODELLING a) Derive equations of motion by using first principle. Consider (if any) system dynamics that need to be neglected, and take into account the assumptions, approximations and simplifications as indicated in the related project pages. b) Linearize the system either by using small angle assumption or Taylor Series expansion, if mathematical description of the system includes non-linear terms. c) Take the Laplace transform of the derived equations by assuming that all the initial conditions are zero. u (0) = u(0)=0 y (0) =ý (0) = 0 xk (0) = k (0)=0 where k = 1,2,...,n n is the number of states d) Obtain the open-loop transfer function of the system G (s) defined between system input U (s) and system output Y (s). Y (s) = G(s) U (s) U(s) G(s) -Y(s)